Operating speed prediction models of trucks at interchange ramps based on high-frequency GPS data
Article Text (Baidu Translation)
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摘要: 为明确互通立交匝道路段货车运行速度规律，在分析高速公路主线至匝道末端货车高频GPS实测数据的基础上，构建了互通立交匝道货车运行速度模型；通过分析货车实测速度，确定了匝道货车运行速度特征点，对特征点处速度可能相关的设计要素进行相关性分析，采用全子集回归方法建立了货车在特征点的多个运行速度模型；对比不同模型的赤池信息量准则、Mallows's Cp统计量以及模型检验值，确定自变量参数，得到了互通立交小鼻点、匝道圆曲线曲中点以及匝道与连接线合流鼻处的货车运行速度预测模型，并采用4条匝道数据对模型进行验证。研究结果表明：互通立交小鼻点、匝道圆曲线曲中点及匝道与连接线合流鼻可作为匝道货车运行速度特征点；匝道圆曲线半径、出口渐变率以及分流点运行速度对小鼻点运行速度有显著影响；半径、曲中点至匝道合流鼻距离以及小鼻点运行速度对曲中点运行速度有显著影响；曲中点前半段纵坡、圆曲线曲率以及曲中点运行速度对合流鼻运行速度有显著影响；3个特征点处的运行速度预测模型相关系数分别为0.988、0.993、0.990，预测值与实测值的平均绝对百分比误差均小于10%，满足模型精度要求。Abstract: To clarify the operating speed rules for trucks at interchange ramps, operating speed models for trucks on interchange ramps were constructed based on the analysis of the measured high-frequency GPS data of trucks from the mainline to the end of the ramp on an expressway. Through the analysis of the measured speeds of trucks, the characteristic points of the truck operating speeds at the ramp were determined, and correlation analysis was carried out for design elements that might be related to the speed at the characteristic points. Multiple operating speed models for trucks at characteristic points were established by using all subsets regression methods. By comparing the Akaike information criterion, mallows's Cp statistic, and model test values of different models, the parameters of the independent variables were determined, and prediction models for truck operating speed at various locations were developed, including the small nose point of interchanges, the midpoint of the ramp curve, and the merging nose of the ramps and the connecting lines. These models were validated by using data from four ramps. Research results show that the small nose point of interchanges, the midpoint of the ramp curve, and the merging nose of the ramps and the connection lines can be considered as the characteristic points of truck operating speed at ramps. The radius of the ramp curve, the gradient rate of the exit, and the operating speed of the diversion point have significant effects on the operating speed at the small nose point. The radius, the distance from the midpoint to the merging nose of the ramp, and the operating speed at the small nose point have significant effects on the operating speed at the midpoint of the ramp curve. The longitudinal slope in the first half of the midpoint, the curvature of the curve, and the operating speed at the midpoint have significant effects on the operating speed at the merging nose. The correlation coefficients of the operating speed prediction models at the three characteristic points are 0.988, 0.993, and 0.990, respectively. The mean absolute percentage errors between the predicted and measured values are less than 10%, which meet the requirements of model accuracy.
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Key words:
- traffic engineering /
- traffic safety /
- operating speed prediction model /
- regression analysis /
- ramp /
- truck
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图 3 匝道货车有效速度数据提取方法
Figure 3. Effective speed data extraction method for on-ramp trucks
图 4 匝道货车有效速度数据处理方法
Figure 4. Effective speed data processing method for on-ramp trucks
图 5 互通立交出口及匝道路段货车速度曲线
Figure 5. Truck speed curves of interchange exit and ramp section
图 7 特征点处速度与变量Pearson相关性分析结果
Figure 7. Results of Pearson correlation analysis between speeds and variables at characteristic points
图 8 模型预测速度与实测速度对比
Figure 8. Comparison between model predicted speeds and measured speeds
表 1 互通立交数据采集路段基本信息
Table 1. Basic information of interchange data collection sections
匝道编号 匝道类型 车道宽/m 匝道圆曲线半径/m 匝道长度/m 1 定向匝道 3.5 120 534.72 2 180 638.82 3 90 557.08 4 100 425.79 5 半定向匝道 160 510.52 6 300 465.10 7 380 459.34 8 环圈匝道 50 443.67 9 60 490.04 10 定向匝道 170 552.59 11 180 486.79 12 半定向匝道 290 480.33 13 环圈匝道 60 463.81 
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表 2 不同类型匝道速度特征对比
Table 2. Speed characteristics comparison of different types of ramp
匝道类型 匝道数量 速度差值范围/(km·h-1) 最小速度位置与匝道特征点关系 定向匝道 4 25~50 圆曲线曲中点前20~25 m 半定向匝道 35~40 匝道终点后40~50 m 环圈匝道 45~50 圆曲线曲中点前20~25 m
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表 3 变量参数统计
Table 3. Variable parameter statistics
变量 匝道编号 1 2 3 4 5 6 7 8 9 Ld/m 90 140 100 100 120 100 100 125 145 Ls/m 83.3 82.7 72.4 59.7 91.2 35.0 82.1 59.5 91.4 Lc/m 128.6 196.3 175.8 86.9 98.2 98.7 209.7 73.9 140.2 L1/m 152.6 186.8 257.5 263.1 85.3 192.2 188.0 59.6 180.0 L2/m 208.3 228.6 169.6 219.7 156.2 142.9 83.2 217.6 249.9 L3/m 118.3 88.6 69.6 119.7 36.2 42.9 -16.8 22.6 104.9 L4/m 48.9 123.2 112.5 24.6 96.7 185.8 172.0 26.1 25.0 K 0.040 0.044 0.010 0.028 0.029 0.014 0.028 0.028 0.039 R1/m 120 180 90 100 160 300 380 50 60 R2/m 2 400 1 989 3 250 9 999 2 000 2 739 9 999 6 000 2 400 R3/m 4 000 5 000 3 000 1 200 2 000 7 000 99 999 99 999 16 000 R4/m 2 800 6 000 2 000 12 000 99 999 99 999 2 000 12 200 99 999 1/R1/m-1 0.008 0.006 0.011 0.010 0.006 0.003 0.003 0.020 0.017 1/R2/m-1 0.000 42 0.000 50 0.000 31 0.000 10 0.000 50 0.000 37 0.000 10 0.000 17 0.000 42 1/R5/m-1 0.008 0.004 0.009 0.010 0.002 0.002 0.008 0.020 0.018 α/rad 1.989 4 1.657 2 3.021 9 1.550 7 1.038 7 0.684 9 0.708 5 2.741 5 3.120 8 i1/% -1.111 -2.542 1.431 3.873 0.477 -0.059 0.305 1.356 -1.080 i2/% 0.601 -0.872 -1.977 -1.01 3.110 1.293 2.780 2.000 -1.859 V0/(km·h-1) 78.67 82.45 73.07 83.05 76.71 82.01 74.82 61.02 82.33 Vd/(km·h-1) 65.69 71.41 61.78 75.13 64.67 75.45 66.85 39.04 66.54 Vq/(km·h-1) 54.91 64.31 54.34 55.71 56.77 70.35 63.80 32.23 46.87 Vz/(km·h-1) 54.03 65.22 49.87 51.58 56.36 69.55 63.67 36.66 46.14
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表 4 运行速度描述性统计
Table 4. Operation speed descriptive statistics
出口匝道货车运行速度 平均值/(km·h-1) 标准差/(km·h-1) 分流点速度 77.128 9 2.351 2 小鼻点速度 65.179 8 3.620 3 曲中点速度 55.481 3 3.701 1 合流鼻速度 54.792 8 3.487 8
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表 5 特征点货车运行速度统计
Table 5. Operation speed statistics of trucks at characteristic points
模型 公式 变量 R2 AIC 1 Vd=93.559－0.244Ld Ld 0.043 44.44 2 Vd=1.397V0－44.785 V0 0.900 27.18 3 Vd=74.776－1 156.244/R1 1/R1 0.506 41.53 4 Vd=7.034+0.959V0－0.146Ld V0、Ld 0.950 25.63 5 Vd=1.152V0－450.984/R1－21.454 V0、1/R1 0.967 21.91 6 Vd=91.769－0.206Ld－307.16/R1 Ld、1/R1 0.517 41.53 7 Vd=1.628V0－379.1K－51.795 V0、K 0.946 26.44 8 Vd=1.26V0－0.093Ld－233.131K－16.081 V0、Ld、K 0.963 25.63 9 Vd=1.326V0－149.04K－462.702/R1－28.446 V0、K、1/R1 0.988 20.23 10 Vd=5.774+0.978V0－0.154Ld+77.728/R1 V0、Ld、1/R1 0.979 21.91 11 Vd=6.474+0.967V0－0.145Ld－617.373/R2 V0、Ld、1/R2 0.954 25.63 12 Vd=1.638V0－374.939K－1 245/R2－52.241 V0、K、1/R2 0.955 26.44 13 Vd=1.25V0－0.094Ld+918.004/R2－234.828K－15.417 V0、Ld、K、1/R2 0.966 25.63 14 Vd=1.292V0－0.104Ld+113.497/R1－236.647K－18.27 V0、Ld、K、1/R1 0.990 20.23 15 Vd=5.443+0.983V0－0.153Ld+76.131/R1－392.81/R2 V0、Ld、1/R1、1/R2 0.988 21.45 16 Vd=1.357V0－0.103Ld+1.644α－254.618K－24.843 V0、Ld、K、α 0.984 25.63 17 Vd=1.329V0－0.061Ld－594.199/R1－267.623K+4.048α－26.19 V0、Ld、K、1/R1、α 0.990 20.23 18 Vd=1.419V0－0.036Ld－870.404/R1－262.804K+5.433α－ 777.611/R2－33.877 V0、Ld、K、1/R1、α、1/R2 0.999 13.26
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表 6 共线性诊断结果
Table 6. Covariance diagnostic results
维数 特征值 条件指数 方差比例 常量 分流点速度/(km·h-1) 匝道圆曲线曲率 出口渐变率 1 3.701 1.00 0.00 0.00 0.01 0.01 2 0.218 4.12 0.00 0.00 0.62 0.04 3 0.079 6.86 0.01 0.01 0.00 0.86 4 0.002 40.32 0.99 0.99 0.37 0.09
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表 7 系数分析结果
Table 7. Coefficient analysis results
自变量 非标准化系数 标准系数 t检验值 显著性 系数的95%置信区间 相关性 共线性统计量 回归系数/截距 标准误差 下限 上限 零阶系数 偏判定系数 部分判定系数 容差 方差扩大因子 常量 -28.446 7.61 -3.74 0.013 -47.99 -8.89 分流点速度 1.326 0.10 0.86 13.81 0.000 1.08 1.57 0.949 0.987 0.683 0.629 1.590 匝道圆曲线曲率 -462.702 111.64 -0.25 -4.15 0.009 -749.68 -175.73 -0.711 -0.880 -0.205 0.669 1.496 出口渐变率 -149.040 51.39 -0.16 -2.90 0.034 -281.13 -16.95 0.046 -0.792 -0.143 0.845 1.183
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表 8 残差诊断结果(部分)
Table 8. Residual diagnosis results (partial)
分流点实测值/(km·h-1) 小鼻点实测值/(km·h-1) 小鼻点预测值/(km·h-1) 残差/(km·h-1) 标准化残差/(km·h-1) 相对误差/% 68.4 54.0 53.569 02 -0.430 976 0.609 163 0.80 72.0 64.8 58.342 62 -6.457 376 -0.841 089 9.97 69.1 57.6 54.497 22 -3.102 776 -0.033 805 5.39 79.2 62.4 67.889 82 5.489 823 2.034 003 8.80 65.3 51.0 49.458 42 -1.541 576 0.341 897 3.02 74.1 63.6 61.127 22 -2.472 776 0.117 804 3.89
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表 9 平均绝对百分比误差计算结果
Table 9. Calculation results of mean absolute percentage error
匝道编号 匝道特征 分流点实测速度/(km·h-1) 小鼻点实测速度/(km·h-1) 曲中点实测速度/(km·h-1) 合流鼻实测速度/(km·h-1) 小鼻点处M/% 曲中点处M/% 合流鼻处M/% 匝道圆曲线半径/m 出口渐变率 10 135 1/25 79.621 68.125 59.279 60.235 3.802 4.893 5.537 11 170 1/24 83.215 73.025 64.983 60.332 4.396 5.281 5.435 12 330 1/24 80.015 73.457 69.352 66.553 4.696 6.549 5.931 13 60 1/25 81.339 65.549 45.877 45.506 6.298 5.713 7.628
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